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IF f(x+f(y))=f(x)+y AA x, y in R and f(0...

IF `f(x+f(y))=f(x)+y AA x, y in R and f(0)=1`, then `int_(0)^(10)f(10-x)dx` is equal to

A

1

B

10

C

`int_(0)^(1)f(x)dx`

D

`10int_(0)^(1)f(x)dx`

Text Solution

Verified by Experts

The correct Answer is:
D
Put y = 0 `rArrf(x+1)=f(x)`
Thus f(x) is periodic with period '1'
`therefore" "int_(0)^(10)f(10-x)dx`
`=int_(0)^(10)f(10-(10-x))dx`
`=int_(0)^(10)f(x)dx`
`=int_(0)^(10)f(x)dx`
`=10int_(0)^(1)f(x)dx`
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